Year: 2026
Type: article
Abstract: The thermalizing dynamics of many-body systems is often described through the lens of the eigenstate thermalization hypothesis (ETH). ETH postulates that the statistical properties of observables, when expressed in the energy eigenbasis, are described by smooth functions, which also describe correlations among the matrix elements. However, the form of these functions is usually left undetermined, constituting a key missing component of the ETH framework. In this Letter, we investigate the structure of such smooth functions by focusing on their Fourier transform, recently identified as free cumulants. Using nonlinear hydrodynamics, we provide a prediction for the universal scaling of the late-time behavior of time-ordered free cumulants in the thermodynamic limit. The prediction is further corroborated by large-scale numerical simulations of several nonintegrable one-dimensional spin models that exhibit diffusive transport behavior. Good agreement is observed in both infinite and finite-temperature regimes and for a collection of local observables. Our results indicate that the smooth multipoint correlation functions within the ETH framework admit a universal hydrodynamic description at low frequencies.
Source: Physical Review Letters
DOI: 10.1103/prv4-948b
Institutions: Osnabrück University, Princeton University, University of Cologne
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: Nichtgleichgewichtsdynamik in 2D Clustern aus der
Perspektive von Quantentypikalität und Eigenzustandsthermalisierung, Klassische und quantenmechanische Arbeitsverteilungen in getriebenen Billards, Korrelationen zwischen Matrixelementen von wenigteilchen Observablen in Energieeigenbasen von vielteilchen Systemen, FOR 2692: Fundamental Aspects of Statistical Mechanics and the Emergence of Thermodynamics in NonEquilibrium Systems, G3356704239, Massivparalleles CPU/GPURechnersystem, G62979356, Quantum Field Theory beyond the Vacuum, TRR 183: Verschränkte Materiezustände, G7399398987, EXC 2004: Materie und Licht für Quanteninformation (ML4Q), Kombinationen gedämpfter harmonischen Oszillationen als stabile Bausteine von Autokorrelationsfunktionen in Quantenvielteilchensystemen
OpenAlex ID: W4417514295